Dynamic error budgeting based robust system and control co-design for active vibration isolation systems

Abstract

This paper proposes a novel method to optimize active vibration isolation systems based on $H_2$-criteria using the dynamic error budgeting framework and $H_{\infty }$ constraints to guarantee robust stability. This method explicitly takes into account all noise sources and disturbances present in active vibration isolation systems. The dynamic error budget is interpreted as an $H_2$ optimal control problem with a specific set of input weighting functions, that are models of the input signal spectra. This is extended with $H_{\infty }$ constraints to guarantee stability robustness of the controller. The constrained optimization problem is solved in a structured control setting, with a non-smooth sub-gradient descent method. This is used to optimize the controller and system parameters simultaneously. First an explorative study is done for a single axis active vibration isolation system, and it is shown that the performance improves significantly relative to a passive vibration isolation system and a benchmark active vibration isolation system. The optimal control formulation is thereafter applied to an experimental system, and performance improvements are obtained by a factor 2.3–4.1 in internal deformation power, and 2.9–13.7 in sensitive payload acceleration power with respect to the previous controller based on engineering intuition.